# All posts by Daniel Scher

# Protect the Sheep

A game of enclosing sheep and wolves in fences helps children to develop their conceptual understanding of polygons.

# A New Twist on Arranging Addends

Of all the original games I've designed, Arranging Addends is among my favorites. On page 1 of the Web Sketchpad model below (and here), you're given five addends—1, 2, 4, 8, and 16—and asked to arrange them in the circles so that the sum of the numbers in each circle matches the values … Continue Reading ››

# Tanton’s Two-Pan Balance Puzzle

I'm a big fan of pan-balance puzzles in which you're given a two-pan balance and asked to use it to uncover a counterfeit coin or determine the weight of a coin. One classic example is the following puzzle:

*You have 12 coins that all look exactly the same. One is counterfeit and is either heavier … Continue Reading ››*

# Splitting Arrays

In last month's Construct a Building post, I presented any array model in which students construct the rooms and floors of a building as a way of representing multiplication. Now I'd like to follow up with a similar array model that allows students to take a problem they don’t know, like 8 × 7, and … Continue Reading ››

# Construct a Building: Modeling Multiplication with Arrays

When Scott Steketee and I developed activities for the Dynamic Number project, we thought about ways that dynamic array models could help children to conceptualize multiplication.

Rather than presenting children with arrays that were fully formed, we thought it would be instructive for them to build these arrays themselves. That design goal led to the … Continue Reading ››

# Adding and Subtracting Fractions on a Number Line

In my previous post, I presented a number line model for adding fractions. Now, I'd like to offer an updated Web Sketchpad fraction model below (and here) with two new pieces of functionality:

- You can subtract as well as add fractions.
- You can divide the number line into equal parts and choose the … Continue Reading ››

# Adding Fractions on a Number Line

In previous posts, I've presented fraction-related Web Sketchpad models from the Dynamic Number project. Several of these activities—specifically Dividing and Subdividing and Deducing the Mystery Fraction —focus on a number-line representation of fractions. Below (and here) is another such websketch, with students constructing segments of fractional length that can be … Continue Reading ››

# A Plethora of Hyperbola Constructions

In my prior blog posts, I've presented methods for constructing ellipses and parabolas using both Web Sketchpad and paper folding. Now it's time for me to finally turn my attention to hyperbolas.

All of the Web Sketchpad models below (and here) are based on the distance definition of a hyperbola: the set of … Continue Reading ››

# Early Childhood Math Routines

Mathematics is a wonderful game. It's one that can stretch students' minds and expose them to the beauty and unexpected delights that lie behind every good problem.

I've always gravitated to colleagues who share my love of math's playful, game-like side, so I quickly made friends with Toni Cameron when we met at P.S. 503 in … Continue Reading ››